Playing a day after deadly attacks killed a total of 14 people in Barcelona and the coastal town of Cambrils in Spain, Muguruza wore a white visor with a black ribbon as a tribute.
"Barcelona te siento. Barcelona I feel you," Muguruza wrote on Twitter after the match.
Muguruza next faces world number one Karolina Pliskova, who won back-to-back matches on Friday.
The Czech first defeated Italian qualifier Camila Giorgi 6-3 4-6 6-0 in a match postponed by a day because of rain.
The top seed then took another step toward successfully defending her title by overpowering former world number one Caroline Wozniacki 6-2 6-4 in her second match.
Pliskova had 27 winners to Wozniacki's eight with only 13 unforced errors compared to the sixth-seeded Dane's 19.
Second seed Simona Halep also beat Britain's Johanna Konta for the first time in an exciting back and forth 6-4 7-6(1) victory.
Halep capitalised on a service break in the first set and then raced out to a 4-1 lead in the second before Konta fought back to send it into a tie-break.
The Romanian, however, dominated the tie-break to set up a semi-final match against American Sloane Stephens.
The American continued her strong form following her return at Wimbledon after an 11-month absence with a foot injury by defeating Germany's Julia Goerges 6-1 7-6(3).
Stephens had earlier beaten Russia's Ekaterina Makarova 2-6 6-3 6-4.
(Reporting by Rory Carroll; ediitng by Ken Ferris)
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